In your original, you were testing if val1, val2, and calc were equal to an empty space. Close up the gaps into just double quotes with no space, so it will return to calculate.htm when no input is inside. You could also apply the function trim(); which will cut off all empty spaces in the front or end of the value. Not sure how lazy you are though.

Okay, here you are comparing two values, if they val1 is greater than val2, it will output the results you have. The problem here is, if both values are the same, it will output your first string "value 1 is greater than Value 2", because when both $results = false; it will use the first line or instruction available, you might want to try something like.

Other than that, your code should be perfectly fine.
Also in your calculate.htm, make sure the values of the fields equal whatever you have them set in this *.php file. Multiply, subtract, add, subtract, etc.